I woke up one night and heard my clock strike “one.” I was too tired to turn on the light to see what time it was. As I lay there pondering, it occurred to me to speculate how long I would have to lie awake in order to be sure what was the exact time.
My clock strikes the hours and strikes “one” each half hour. I fell asleep before I solved the problem, but can you work out what is the longest time I would have to lie awake after hearing the strike “one,” to be sure of the time?
You will have to lie awake for 1 hour to be sure of the time.
The strike you heard was either 1:00 AM or some half hour. If, after another half hour you hear two or more strikes, you know what hour it is, but if you again hear one strike, you may have heard successively 12:30 AM and 1:00 AM or 1:00 AM and 1:30 AM.
After another half hour you either hear 1 strike (1:30 AM) or two strikes (2:00 AM).